The available minimum variance (MV) benchmarks do not take the controller structure into account and thus can lead to incorrect conclusions regarding the performance of decentralized controllers. In this paper, we present a method for computing a lower bound on the least output variance achievable using decentralized controllers, where the nonconvexity of the optimization problem is handled using sums of squares programming. Though tight, the computation of this lower bound requires that the process model be known. As a more practical approach, we derive an MV benchmark for performance assessment of decentralized controllers on a loop by loop basis. The MV benchmark for loop by loop analysis can be estimated from the closed loop operating data with the knowledge of time delays between all the inputs and outputs. The usefulness of the proposed benchmarks is demonstrated using simulation examples.